At 10 o'clock the hands of a clock make an acute angle and a reflex angle. Find the measure of each of these angles.

A clock is a circle of 360°, divided into 12 hours. Therefore, each hour gap represents:

$\dfrac{360^\circ}{12} = 30^\circ$

Acute Angle:

At 10 o'clock, the minute hand is at 12 and the hour hand is at 10. The shortest distance between them is 2 hour gaps (from 10 to 11, and 11 to 12).

∴ 2 x 30° = 60°

Reflex Angle:

This is the larger outer angle between the two hands.

∴ 360° - 60° = 300°

The acute angle is 60° and the reflex angle is 300°.